An Example of "Boot Strapping" In Applied Physics
In mathematical physics a number of specialized techniques are learned with the passage of time, techniques which become part of an applied physicist's box of magic. One technique is colloquially known as "Boot Strapping", by which a minimum of data can be used to yield a maximum of results. Sometimes this involves taking a series of under described equations (say a single equation in two unknowns), some additional good data points and a technique to more fully analyze the problem.
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In Geophysics there is a nice example of "Boot Strapping" in how one can estimate both the speed of a shot wave in seismic imaging, and the depth of an interface or feature within the earth. This practical seismic imaging example is well suited for a first year physics course studying wave motion.
While this example is known by any geophysicist worth their weight in rock, it is nonetheless a good practical example to introduce the "Boot Strapping" technique to freshman physics students (while we have one equation with two unknowns, a little ingenuity helped you to get around that limitation). This example is also good for showing that algebraic and geometric techniques many times complement each other.